Lecture10 - Lecture #10 Recall that an isocline is an...

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Lecture #10 As we said at the end of Lecture #9, isoclines can be straight or Recall that an isocline is an output expansion line with a constant MRTS. curved. Straight isoclines are graphical representations of a homogeneous production function, while curved isoclines are graphical representations of non-homogeneous production functions. K K Isocline (K/L constant) y 2 y 1 y 2 y 1 Isocline (K/L varies) LL
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K K Isocline (K/L constant) y 2 y 1 y 2 y 1 Isocline (K/L varies) L L Along a straight isocline, factor intensity remains constant (K/L). Along a curved isocline, factor intensity changes. In the graph bove production becomes more Thus, the production function is homogeneous (the shape of the isocline depends only on capital above production becomes more labour intensive…as output increases K/L is falling) and labour). In this case, the production function is not homogeneous (the shape of the isocline depends on ther factors besides just capital other factors besides just capital and labour).
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A production function is homogeneous when a multiple of inputs can be factored out. For example: Suppose we have a production function defined as Y = K + L Then … 2K + 2L = 2(K + L) = 2Y When the factor by which we increase the inputs is equal to the factor by which output increases as a result, then the production function is said to be linearly homogeneous (homogeneous of degree one). We will be dealing almost exclusively with isoclines that are linearly homogeneous, that is, when inputs double the effect on output is that output doubles. This feature of the production function is called constant returns to scale. K DRS K IRS K CRS y 2K 2K B y 2K B y 2y L 1K 1L 2L A B y 2y L 1K 1L 2L A y 2y L 1K 1L 2L A
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K CRS K IRS K DRS 2K B 2K B 2K y 2y 1K L L A y 2y 1K L L A y 2y 1K L L A B L 1L 2L L 1L 2L L 1L 2L If we double inputs, output doubles. The production If we double inputs, output more than doubles. The If we double inputs, output less than doubles. The function is linearly homogeneous or displaying constant turns to scale production function is said to display increasing returns to scale. production function is said to display decreasing returns to scale. returns to scale. It takes less than double the inputs to double the output. It takes more than double the inputs to double the output. There is another way to think about this concept. Along the following isocline (next slide), returns to scale are increasing at first and then they eventually decrease.
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Up to point B, the production K isocline function displays increasing returns to scale (inputs double, output more than doubles). After B, the production function displays 4 D Y=9 decreasing returns to scale (inputs increase in a certain proportion, but outputs increases in a smaller proportion). We can see, for lt h t i f f A t C 2 3 B C Y=8 example, that if we move from A to C (triple inputs) we less than triple output. Similarly, if we move from A to D (quadruple inputs) we less than adr ple o tp t 1 A =3 Y=7 quadruple output.
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Lecture10 - Lecture #10 Recall that an isocline is an...

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